Engineers at Exponent were tasked with studying the air pressure of footballs at its test complex in Phoenix in the aftermath of the N.F.L.’s Deflategate scandal.CreditCreditCaitlin O'Hara for The New York Times

The Deflategate Scientists Unlock Their Lab

The researchers whose work led to Tom Brady’s suspension have never spoken publicly. Now they’re eager to say they were right, no matter what Patriots fans believe.

Engineers at Exponent were tasked with studying the air pressure of footballs at its test complex in Phoenix in the aftermath of the N.F.L.’s Deflategate scandal.CreditCreditCaitlin O'Hara for The New York Times

PHOENIX — It was over 100 degrees in the scrubby sprawl on the city’s northern frontier earlier this month, but inside the 40-foot-long thermal chamber, it was 48 degrees — same as it was for the playoff game on that January night in Foxborough, Mass. The floor was covered in green artificial turf, like a football field.

Through a side door was a similarly stark and windowless space, this one at room temperature, the same setting as the officials’ locker room in Gillette Stadium, home of the New England Patriots, about 2,300 miles away.

From the outside, the chamber looks like a long storage container plopped on a pavement wasteland behind two seemingly ordinary office buildings. John Pye, a 46-year-old aerospace engineer born and raised in Canada, walked the distance in the glaring light and baking heat of midday and pulled a large door handle, like that on a walk-in freezer.

“We’re heading into where we spent about three months of our lives a year and a half ago,” Pye said.

And suddenly he was transported to another time, another place, when (and where) N.F.L. footballs and air pressure were all the rage.

The 2016 season has started without the Patriots’ star quarterback, Tom Brady, who is serving a four-game suspension for his role, murky as it may be, in Deflategate. Brady and the Patriots were ensnared in a contentious investigation to determine if, for the A.F.C. championship game in January 2015, against the Indianapolis Colts, they conspired to purposely deflate their game-day footballs below league standards for Brady’s benefit.

Part of the reason Brady is not playing now is what Pye and his co-workers found then — or, more precisely, could not find: a plausible scientific explanation for why the Patriots’ balls were not fully inflated.

“I would feel bad if I thought I made a mistake or I thought I overlooked something,” Pye said. “But we made measurements and put the facts out, and it went from there.”

Deflategate swept a nation into debates over science (the Ideal Gas Law) and culture (cheating in sports), from the predictable (Can the N.F.L. be trusted? Can the Patriots?) to the less so (What is the effect of vigorous rubbing on a football?). Arguments were clouded by allegiances and conspiracy theories, reports and rumors.

But it was here, in the temperature-controlled silence of a desert bunker, that Pye oversaw months of experiments to try to determine if air was intentionally removed from the footballs, or if the recorded levels could be explained by science.

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John Pye at Exponent’s test facility in Phoenix, where he oversaw months of experiments to determine whether air was intentionally removed from footballs used by the Patriots, or if the recorded air pressure levels could be explained by science.CreditCaitlin O'Hara for The New York Times

When the results of the N.F.L.’s investigation were released in May 2015, the sports world devoured it. It was called the Wells report, and the first half of it was filled with circumstantial evidence of foul play and delicious components of a great mystery.

There was the setting, in a modern American castle, the home stadium of the league’s top franchise. There was no dead body, but a pile of game-used footballs. There was no smoking gun, but there were conflicting pressure gauges. There was a famous athlete linked to shadowy ball boys by text messages that hinted at a cover-up. There were bungling investigators (game officials) and an unexplained bathroom stop. There was even a rainy night.

Like an ink blot, it became whatever anyone wanted to see.

The second part of the Wells report did not receive the full brunt of attention initially. It was a wonky scientific document filled with equations, tables and graphs, linked by explanations of experimental methods and laws of physics. It was 68 pages, plus a six-page executive summary at the beginning and a nine-page appendix at the end. The title pages said that it was “prepared by” a company called Exponent, of Menlo Park, Calif.

Pye was one of four primary scientists and engineers leading Exponent’s investigation. Exponent “identified no set of credible environmental or physical factors that completely accounts for the additional loss in air pressure.” It did not say that someone deliberately removed air from the footballs, but it might as well have.

Soon enough, the Exponent report, too, was submerged by scrutiny. With the name of the firm and the men responsible for producing it now public, the attacks came from swarms of Patriots fans, which was to be expected. More surprising, at least to Exponent, the work was pulled apart by other scientists. Several went public with their critiques.

Exponent heard and read it all and said nothing, maintaining what it calls “professional silence” until the entire matter was resolved. That took more than a year of hearings and appeals and talk of Brady taking the case to the United States Supreme Court.

Now that Brady has accepted his punishment and is sitting out, Exponent is finally talking. And it wants everyone to know: It was right all along.

“When we released the report, I stood behind it 100 percent,” Gabriel Ganot, one of the four Exponent executives to lead the Deflategate investigation, said. “Having heard whatever everybody has said, and having reviewed the thoughts of the critics, I still stand behind it 100 percent.”

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Patriots quarterback Tom Brady is serving a four-game suspension after an inquiry commissioned by the N.F.L. concluded that it was “more probable than not” that Patriots employees were deliberately releasing air from footballs and that Brady knew about it.CreditDamon Winter/The New York Times

Forming the Team

Pye was in his corner office in Phoenix when he got a call from New York. It was Robert Caligiuri, 65, a principal engineer who has worked at Exponent for nearly 30 years and is one of Pye’s mentors.

Caligiuri stood alongside Ganot, 32, a materials engineer, in the lobby of the Midtown Hilton. They had just finished a meeting a block away at the New York offices of Paul, Weiss, Rifkind, Wharton & Garrison, the law firm hired by the N.F.L. to investigate the fast-spreading wildfire already known as Deflategate.

The law firm needed someone to investigate the science portion of the scandal. One of Ganot’s former professors at Columbia recommended Exponent.

At the time, Pye was working on a project for Britain’s Ministry of Defense, designing robot-driven Land Rovers fitted with ground-penetrating radar systems to detect improvised explosive devices in the Middle East.

“John, we need you to do these tests for us,” Pye recalled Caligiuri saying. “It’s footballs. I’m going to give you some pressures and I’m going to give you some scenarios, temperatures and environment, and I need you to do some tests.”

Pye smiled at the memory.

“It always starts with ‘some tests,’” he said.

Caligiuri passed along the basics: The Patriots’ footballs were thought to be pumped up to about 12.5 p.s.i. before the game, the Colts’ balls at 13 p.s.i. The halftime readings were much lower and varied. The temperature outside was 48 degrees. It was known that the balls were tested at halftime inside, at room temperature: 11 Patriots balls but only four Colts balls, because officials ran out of time. The referee had two gauges, and one was way off.

Pye was still on the phone when he started plugging numbers into the Ideal Gas Law: PV = nRT. Pressure drops with temperature. The balls would, of course, be deflated by halftime, to some degree.

“My impression from the very first phone call was that this was going to be an explainable thing,” Pye said.

Caligiuri called Duane Steffey, 55, a principal scientist for Exponent with a Ph.D. in statistics. He added him to the team, too.

“Is there a real difference here?” Steffey said. “Because we were about to embark on a significant investigation, and if all of this is within the noise level, and within a margin of error, then there’s really nothing here. So that’s the first thing we did.”

Within a day or two, it was clear: The numbers were statistically significant. They could not be fully explained within accepted error margins.

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Robert Caligiuri, an engineer who has worked at Exponent for nearly 30 years, sensed his company’s report would be scrutinized. “We knew we needed to be totally bulletproof here,” he said.CreditJason Henry for The New York Times

By then, the public was already debating the effect of that night’s rain, whether balls lost air when they were used, and the fact that the Patriots were on offense more in the first half. New England Coach Bill Belichick held a news conference to suggest that the “rubbing process” might explain everything.

“We knew this was going to get a lot of scrutiny, from your eighth-grade science classes to your physics professors,” Pye said. “So we wanted to try to answer all those questions.”

The conference room at Exponent’s Phoenix laboratory has vast windows overlooking the mostly shadeless landscape. About 10 scientists and engineers gathered around the room’s oval table and tossed around ideas, which were written on a whiteboard.

“Everything we can think of,” Pye said. “Whether it’s human related, environment related, physics related, materials related, including the football and the gauge itself. We tackle the measurements, we tackle the environment, we tackle the inflation side. And we write this all down, kind of group them, think of ways we can refine this model. And then I get back on the phone to Bob. He’s back to Menlo Park at this point, and I said, ‘Bob, we’ve got a plan.’”

Caligiuri, a grandfather with a trim white mustache, oversaw everything. Steffey handled the statistics. Pye handled the experiments. Ganot was the go-between, making six trips to Phoenix in the course of a couple of months.

Not all of Exponent’s work receives public scrutiny, but Caligiuri knew this would, maybe as much as anything.

“We knew there would be controversy here,” Caligiuri said. “And we needed absolutely the best people we could possibly put on it. That’s why I organized it the way I did. I knew the way to approach this — and frankly we had seen the news, we saw the people blaming it on the way he rubbed the footballs and people talking about it and stuff — and we knew that there were some questionable things out there already. So we knew we needed to be totally bulletproof here.”

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The U-shaped headquarters of the engineering firm Exponent, in Menlo Park, Calif.CreditJason Henry for The New York Times

6,000 Projects a Year

The U-shaped, three-story Exponent headquarters in Menlo Park is about 10 miles from where Tom Brady went to high school. It is fronted by a shallow rectangular pool whose primary feature is a twisted, blue steel beam bent into a loop, like an unfamiliar cursive letter. It was part of a 2,000-foot television transmission tower in Missouri that collapsed during repairs in 1988. Some of the falling beams, 35 feet long and five inches in diameter, buried themselves 40 feet into the ground. Exponent investigated the accident.

In the lobby are oil paintings of two of the five Stanford professors who started the company as Failure Analysis Associates. The company built its reputation on large-scale disasters — crashed planes, exploded oil rigs, burst pipelines, fallen buildings. One of the paintings is of Alan Tetelman, wearing a bushy 1970s-style mustache and a shirt with the sleeves rolled up. He was president in 1978 when, on his way to investigate a plane crash, he was killed in a plane crash.

The company now employs more than 1,000 people working out of 20 offices, including two in Asia and two in Europe. It went public in 1990 (its ticker symbol was FAIL), changed its named to Exponent in 1998 (ticker symbol: EXPO), and reported revenue of nearly $313 million last year.

Exponent’s work force includes nearly 500 employees with doctorates. They include physicists, metallurgists, epidemiologists, automotive engineers and data scientists.

“Everything from A to Z,” Caligiuri said. “Architects to zoologists. I think we still have a zoologist.”

The work is now fairly divided between “reactive” investigations (what went wrong) and “proactive” projects (product development). For the latter, having its headquarters in Silicon Valley — Facebook headquarters is a mile away — was a stroke of good fortune for Exponent. To get an idea of the breadth of companies that have hired Exponent, Caligiuri said, “look at the Fortune 500.”

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A peek into some of the labs at Exponent’s headquarters, top row, in Menlo Park, Calif., and its testing complex in Phoenix, bottom row.CreditTop row, Jason Henry for The New York Times; bottom row, Caitlin O'Hara for The New York Times

Exponent certainly has its critics. It is often hired by insurance companies and companies in duress, perhaps facing lawsuits and the prospect of monstrous recalls and payouts. And when those companies receive research from Exponent that supports their claims — that says they or the company they insure were not at fault, for example — they often use the research to bolster their case, in courtrooms and in the court of public opinion.

Exponent investigated the collapse of the Twin Towers for Swiss Re, one of the World Trade Center’s major insurers, after Sept. 11. It was hired by Exxon after the Valdez oil spill and by BP after the Deepwater Horizon explosion. NASA hired Exponent after the space shuttle disasters. The Department of Justice hired Exponent after the Oklahoma City bombing.

Automobile companies routinely hire Exponent to provide backup investigations during scandals, one reason Exponent’s 150-acre complex in Phoenix includes a two-mile oval track, for testing — and crashing — cars and other vehicles. Exponent’s research and experts have sided with the likes of Suzuki (with rollover worries about its Samurai) and Toyota (unintended acceleration). A 2013 Exponent investigation into a long fight over ignition switches in General Motors cars helped lead to a widespread recall.

Such public and controversial cases are a small part of what Exponent does. It works on 6,000 projects each year for 2,000 clients. But some have given Exponent a reputation as a “hired gun,” as The Los Angeles Times called Exponent in 2010 — a company that will provide scientific affirmation and gravitas for a price.

Exponent staunchly denies that its scientific favor can be bought. It says that it is just as likely that its research runs counter to its clients’ hopes, but that research then gets tucked away, never to see the light of day.

“Clients hire Exponent because of our reputation for our independent, high quality, thorough and objective technical and scientific evaluations,” Exponent’s chief executive, Paul Johnston, said in an email. “We frequently give results to clients that are not what they would have wished, which can often be seen through the resulting product recalls.”

The first-floor hallways of Exponent’s California headquarters are lined with laboratories, all accessible only with an electronic card. There is a biomedical lab with a bone-cutting saw. There is a fluids lab with a combustion chamber. There is a chemistry lab, a photonics lab, a chromatography lab. There are X-ray machines, CT scanners and two scanning electron microscopes.

Client confidentiality is a major issue. To prepare for a visit from a journalist and a photographer, Exponent employees covered a couple of in-progress, large-scale experiments in blue tarps. A 3-D printer in the prototype room was hidden behind paper while it hummed and buzzed.

Out a side door, where the traffic from nearby Highway 101 could be seen and heard, a warehouse is filled with objects from prior experiments. Ganot described it as the warehouse from the final scene of “Raiders of the Lost Ark,” but would not permit a look inside. Outside, in the sun, the ground was covered in metal parts and enormous gas pipes, some of them burst, all of them there to be studied because something had gone wrong. A car nearby was covered in a tarp, unidentifiable.

It might be strange, then, that a company that covets discretion and is known, if at all, for investigating disasters that often kill people and can cost billions of dollars in damages, would want to tackle something as mundane and inconsequential as the air inside N.F.L. footballs.

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Client confidentiality is a major issue at Exponent. A test was conducted behind a curtain during a visit by a reporter and a photographer.CreditCaitlin O'Hara for The New York Times

“The visibility of this project fits into some of the largest that we do at this firm,” Pye said. “But when you think about the impact? Meh. Not so much. No one is losing their lives here. The building is not burning down. The vehicle is not crashing. The product is still working. Nothing’s caught on fire.”

So why even get involved?

“It’s an interesting scientific problem,” Caligiuri said. “It clearly was not as simple as what it was portrayed in the early days. Frankly, it could be controversial, but we are not afraid of controversial matters.”

A Gillette Stadium Simulator

The temperature inside the thermal chamber at Exponent’s highly secured laboratories in Phoenix can be set anywhere from minus 10 degrees Celsius (14 degrees Fahrenheit) to 60 (140 degrees Fahrenheit).

Depending on the day, it might hold a car or a truck or batteries or personal electronics or something else that someone wants to test for performance in extreme conditions. In early 2015, during the N.F.L. playoffs, it was filled with hot tubs.

Then the Patriots beat the Colts and the Deflategate scandal began. Thousands of fans and media members converged on Arizona for the Super Bowl in the Phoenix suburb of Glendale, unaware that the cold conditions at New England’s Gillette Stadium soon would be reconstructed in a thermal lab in the desert a few miles away.

Pye was in charge. He is a gregarious man with the air of a suburban dad. He did not play football but looks as if he could have. Pye and his wife have a son and a daughter, and their son plays football for the freshman team at his high school.

Now Pye can perform a good party trick. Toss him a football and ask about its pressure.

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John Pye stood for a portrait in a lab used for some of the Deflategate experiments.CreditCaitlin O'Hara for The New York Times

“I’ll say 12.3,” he said, squeezing one. He stuck a gauge in it and showed the digital result: 12.25.

Pye was born in Kamloops, British Columbia, but his family moved frequently because his father managed hotels. Pye ended up in Florida for high school, then back to the University of Toronto for a degree in engineering science. He earned a master’s degree and a doctorate in aerospace engineering at Stanford. That led him to nearby Exponent, where much of Pye’s work involves robotics and the military. Since 2005, Pye, now an American citizen, has overseen Exponent’s Test and Engineering Center on the far northern edge of Phoenix.

“What we do here is the big stuff,” Pye said.

Exponent could have investigated footballs just about anywhere. But Phoenix had a big thermal chamber. It had Pye. And was just about as far from New England as could be.

“A rule we enforced on ourselves is that we had to control for football-fan bias,” Pye said. “So we specifically did not involve our Boston office.”

Ganot went to Gillette Stadium to examine the scene of the alleged football crime. He wanted to understand the space between the field and the officials’ locker room, since temperature transitions were an important part of the experiments. He wanted to examine the room’s heating and cooling system, the reliability of its thermostat, the consistency of the room conditions.

The locker room in Arizona was roughly the same size as the one in Gillette Stadium and was set to match the known conditions from the game. Next door, the floor of the “field” was covered in artificial turf. It was not merely decoration. Pye wanted something that could get wet so that when the balls hit the ground, they would pick up moisture, just as they did on that cold, wet night in Massachusetts.

The experiments began with the two gauges used by the referee Walt Anderson — one called the “logo” gauge, with a Wilson logo on it, the other the “non-logo” gauge. One gave relatively accurate pressure readings, while the other read significantly higher, adding to the cloud of confusion over Deflategate.

Pye’s nine-member team analyzed the gauges and compared them to 50 others of the same model. They tested the potential effects of temperature, various ball pressures and battery life. Did it matter that one had a longer needle? (No.) Did it matter who used them? (No.)

Analysis of the gauges consumed 18 pages of the report. Among its conclusions was that the gauges used were different, but consistently different.

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Pye and his team tested things like the potential effects of temperature and battery life on the air pressure gauges.CreditCaitlin O'Hara for The New York Times

About half of the report was devoted to “physical, usage, and environmental effects.” Did the balls lose air when used in the game? (According to automated squeezing tests with 650 pounds of force administered 1,000 times, no.) Does vigorous rubbing matter? (Yes, but the effect wears off in 30 minutes, long before the officials would have tested the air pressure before the game.)

As part of those experiments, Pye set up a television replaying the game in real time. Exponent employees imitated what they watched — throwing the balls, falling on them, shuffling them out of play, wiping them with towels, spraying them with water to simulate rain.

“He was the head ball boy,” Pye said, nodding to an employee named Daniel Kingsley.

The trickiest part of the investigation, and where there remains the most debate, was over the timing of the measurements taken at halftime. The Ideal Gas Law and Gay-Lussac’s law are among those that explain how much the air pressure inside something like a football decreases with colder temperatures and increases with warmer ones.

The tougher question facing Deflategate investigators was determining how quickly the internal temperature and pressure of the balls would have changed as the environment changed. And while officials recorded the order of balls as they were measured during about 13 minutes of halftime — Patriots’ balls first — the exact timing was unclear.

“If you waited forever in the locker room before you took the halftime measurements, they should be the same,” Pye said. “The issue was that it was something less than that.”

For weeks, Pye and his team ran tests, ball by ball, gauge by gauge, game simulation after game simulation, trying to account for all the possibilities.

In the end, Exponent said that it could not “determine with absolute certainty” whether there had been tampering with New England’s balls. The insinuation was more damning.

“We conclude that within the range of game characteristics most likely to have occurred on Game Day, we have identified no set of credible environmental or physical factors that completely accounts for the additional loss in air pressure exhibited by the Patriots game balls as compared to the loss in air pressure exhibited by the Colts game balls,” the report said.

“If we had the exact same report and would have said the pressures are explainable, you never would have heard anything about it,” Pye said. “The N.F.L. would have said, ‘Oh, O.K., and moved on.’ You wouldn’t have heard about Exponent, you wouldn’t have heard about John Pye, you wouldn’t have heard about all the things that happened from then.”

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A fan urged the Patriots to focus on winning the Super Bowl at a send-off rally in Boston in January 2015.CreditMaddie Meyer/Getty Images North America

Exponent submitted the report to Paul, Weiss, the law firm in New York. There had been little interaction between the coinciding investigations — one featuring dozens of interviews and analysis of text messages and fascinating behind-the-scenes accounts and entanglements, and Exponent’s dive into the science of air pressure.

(One exception came when Paul, Weiss asked Exponent if it was possible for someone to take a bag of 12 footballs into a bathroom and deflate them, at least a little, in 1 minute 40 seconds. A Patriots ball boy was seen taking balls into the bathroom on the way to the field before the game, and it became the primary theory for how the balls lost their air pressure. Pye found a small office and had several Exponent employees try. Yes, definitely, he told the lawyers in New York.)

On May 6, 2015, the N.F.L. released what instantly became known as the Wells report, named for the lead lawyer in the investigation, Theodore V. Wells Jr. It concluded that it was “more probable than not” that Patriots employees were deliberately releasing air from footballs and that Brady knew about it.

It was prominent news. And as people dug deeper into the report, past the juicy circumstantial evidence, and dipped into the science and data of Exponent’s analysis, the Ideal Gas Law had its talk-radio moment. Professors and other scientists questioned Exponent’s findings. Columnists tore into Exponent’s credentials. The “hired gun” headlines returned.

Exponent officials heard it and read it all. They remained silent as their reputation took shot after shot.

“That was difficult,” Caligiuri said. “There’s always an urge to respond to critics.”

Pye put the critics into three categories. One was the unabashed fan who was “going to make the call on feeling over questions of fact.”

“That doesn’t bother me at all,” Pye said. “That’s just the world we live in.”

Second were the armchair scientists, those who understood enough to raise reasonable questions, usually quickly dismissed. Exponent anticipated them in this case, which is one reason it conducted every experiment it could think of, even if it knew the answers. “We tried to head those people off,” Pye said.

Third were Exponent’s peers, the usual audience for Exponent’s work. They are the ones who frustrate Exponent most.

“The real world is the real world — it’s not a binary thing,” Pye said. “Binary is a human invention; the real world has a continuum. So you need to understand where your work fits on that continuum. To those people, we wanted to provide enough data so that they could understand what we did, but also understand the significance of what we did. What I found, in a lot of criticisms, is that subtlety, that significance piece, was missed.”

Caligiuri was more direct.

“What disappoints me the most from the scientific community is they said we didn’t do things that we did,” he said. “And it’s in the report. I believe in the scientific method. I believe in challenging what people say. That’s all part of the verification and validation process. I have no problem with that. But if you’re going to look at what someone else has put forward as a hypothesis, a theory or experimental verification, you have to understand what they did, and then work from there. And I’m not sure that everybody did that.”

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Roger Goodell, the N.F.L. commissioner, arriving at federal court for a hearing over Brady’s suspension in Manhattan in August 2015.CreditSpencer Platt/Getty Images

A rare chance to set the record straight came at an appeal hearing for Brady at the N.F.L.’s New York offices. Caligiuri and Steffey were among the others questioned and cross-examined.

“The hearing was somewhat therapeutic,” Steffey said.

Exponent still receives emails from adamant critics, and its role in Deflategate has cost it several prospective clients, the company said. At least one in the Northeast told Exponent that it could not risk its own credibility by being associated with the company behind the controversial Deflategate science.

But there are no regrets. Brady is sitting out his suspension, and Exponent has moved on. The thermal chamber still has its artificial turf, but it now is testing lithium-ion batteries, not footballs.

“The thing that I wanted to make sure came out when we were no longer quiet was that there’s real science here,” Pye said. “There’s real engineering. We didn’t start from feelings. We started from facts — the facts that we had, which were complete to the degree that they were complete. And we took those as far as we thought science and engineering could take them. And then presented that.”

Pye opened the metal door of the chamber. He stepped out of the New England winter night and into the afternoon blast of an Arizona summer.

Correction:

An earlier version of this article misstated the distance from Phoenix to Foxborough, Mass. It is about 2,300 miles, not 3,500.

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